internal/ceres/numeric_diff_test_utils.h

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#ifdef CERES_HAS_GTEST

#ifndef CERES_INTERNAL_NUMERIC_DIFF_TEST_UTILS_H_
#define CERES_INTERNAL_NUMERIC_DIFF_TEST_UTILS_H_

#include <random>

#include "ceres/cost_function.h"
#include "ceres/internal/export.h"
#include "ceres/sized_cost_function.h"
#include "ceres/types.h"

namespace ceres::internal {

// Noise factor for randomized cost function.
static constexpr double kNoiseFactor = 0.01;

// Default random seed for randomized cost function.
static constexpr unsigned int kRandomSeed = 1234;

// y1 = x1'x2      -> dy1/dx1 = x2,               dy1/dx2 = x1
// y2 = (x1'x2)^2  -> dy2/dx1 = 2 * x2 * (x1'x2), dy2/dx2 = 2 * x1 * (x1'x2)
// y3 = x2'x2      -> dy3/dx1 = 0,                dy3/dx2 = 2 * x2
class CERES_NO_EXPORT EasyFunctor {
 public:
  bool operator()(const double* x1, const double* x2, double* residuals) const;
  void ExpectCostFunctionEvaluationIsNearlyCorrect(
      const CostFunction& cost_function, NumericDiffMethodType method) const;
};

class EasyCostFunction : public SizedCostFunction<3, 5, 5> {
 public:
  bool Evaluate(double const* const* parameters,
                double* residuals,
                double** /* not used */) const final {
    return functor_(parameters[0], parameters[1], residuals);
  }

 private:
  EasyFunctor functor_;
};

// y1 = sin(x1'x2)
// y2 = exp(-x1'x2 / 10)
//
// dy1/dx1 =  x2 * cos(x1'x2),            dy1/dx2 =  x1 * cos(x1'x2)
// dy2/dx1 = -x2 * exp(-x1'x2 / 10) / 10, dy2/dx2 = -x2 * exp(-x1'x2 / 10) / 10
class CERES_NO_EXPORT TranscendentalFunctor {
 public:
  bool operator()(const double* x1, const double* x2, double* residuals) const;
  void ExpectCostFunctionEvaluationIsNearlyCorrect(
      const CostFunction& cost_function, NumericDiffMethodType method) const;
};

class CERES_NO_EXPORT TranscendentalCostFunction
    : public SizedCostFunction<2, 5, 5> {
 public:
  bool Evaluate(double const* const* parameters,
                double* residuals,
                double** /* not used */) const final {
    return functor_(parameters[0], parameters[1], residuals);
  }

 private:
  TranscendentalFunctor functor_;
};

// y = exp(x), dy/dx = exp(x)
class CERES_NO_EXPORT ExponentialFunctor {
 public:
  bool operator()(const double* x1, double* residuals) const;
  void ExpectCostFunctionEvaluationIsNearlyCorrect(
      const CostFunction& cost_function) const;
};

class ExponentialCostFunction : public SizedCostFunction<1, 1> {
 public:
  bool Evaluate(double const* const* parameters,
                double* residuals,
                double** /* not used */) const final {
    return functor_(parameters[0], residuals);
  }

 private:
  ExponentialFunctor functor_;
};

// Test adaptive numeric differentiation by synthetically adding random noise
// to a functor.
// y = x^2 + [random noise], dy/dx ~ 2x
class CERES_NO_EXPORT RandomizedFunctor {
 public:
  RandomizedFunctor(double noise_factor, std::mt19937& prng)
      : noise_factor_(noise_factor),
        prng_(&prng),
        uniform_distribution_{-noise_factor, noise_factor} {}

  bool operator()(const double* x1, double* residuals) const;
  void ExpectCostFunctionEvaluationIsNearlyCorrect(
      const CostFunction& cost_function) const;

 private:
  double noise_factor_;
  // Store the generator as a pointer to be able to modify the instance the
  // pointer is pointing to.
  std::mt19937* prng_;
  mutable std::uniform_real_distribution<> uniform_distribution_;
};

class CERES_NO_EXPORT RandomizedCostFunction : public SizedCostFunction<1, 1> {
 public:
  RandomizedCostFunction(double noise_factor, std::mt19937& prng)
      : functor_(noise_factor, prng) {}

  bool Evaluate(double const* const* parameters,
                double* residuals,
                double** /* not used */) const final {
    return functor_(parameters[0], residuals);
  }

 private:
  RandomizedFunctor functor_;
};

}  // namespace ceres::internal

#endif  // CERES_INTERNAL_NUMERIC_DIFF_TEST_UTILS_H_

#endif  // CERES_HAS_GTEST